@article{PhysRevE.108.064212,
title = {Exposing hypersensitivity in quantum chaotic dynamics},
author = {Andrzej Grudka and Paweł Kurzyński and Adam S Sajna and Jan Wójcik and Antoni Wójcik},
url = {https://link.aps.org/doi/10.1103/PhysRevE.108.064212},
doi = {10.1103/PhysRevE.108.064212},
year = {2023},
date = {2023-12-01},
journal = {Phys. Rev. E},
volume = {108},
pages = {064212},
publisher = {American Physical Society},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

@article{grudka23-2,
title = {Complementarity in quantum walks},
author = {Andrzej Grudka and Paweł Kurzyński and Tomasz P Polak and Adam S Sajna and Jan Wójcik and Antoni Wójcik},
doi = {10.1088/1751-8121/acdcd0},
year = {2023},
date = {2023-06-19},
journal = {Journal of Physics A},
volume = {56},
pages = {275303},
abstract = {The eigenbases of two quantum observables, {|ai⟩}Di=1 and {|bj⟩}Dj=1, form mutually unbiased bases (MUB) if |⟨ai |bj⟩| = 1/
√D for all i and j. In realistic situations MUB are hard to obtain and one looks for approximate MUB (AMUB), in which case the corresponding eigenbases obey |⟨ai |bj⟩| ⩽ c/√D, where c is some positive constant independent of D. In majority of cases observables corresponding to MUB and AMUB do not have clear physical interpretation. Here we study discrete-time quantum walks (QWs) on d-cycles with a position and coin-dependent phase-shift. Such a model simulates a dynamics of a quantum particle moving on a ring with an artificial gauge field. In our case the amplitude of the phase-shift is governed by a single discrete parameter q. We solve the model analytically and observe that for prime d the eigenvectors of two QW evolution operators form AMUB. Namely, if d is prime the corresponding eigenvectors of the evolution operators, that act in the D-dimensional Hilbert space (D = 2d), obey |⟨vq|v ′q ′ ⟩| ⩽√2/√D for q ̸= q ′ and for all |vq⟩ and |v ′q ′ ⟩. Finally, we show that the analogous AMUB relation still holds in the continuous version of this model, which corresponds to a one-dimensional Dirac particle.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

@article{grudka23,
title = {Topological invariants in quantum walks},
author = {Andrzej Grudka and Marcin Karczewski and Paweł Kurzyński and Jan Wójcik and Antoni Wójcik},
doi = {10.1103/PhysRevA.107.032201},
year = {2023},
date = {2023-03-01},
journal = {Physical Review A},
volume = {107},
pages = {032201},
abstract = {Discrete-time quantum walks (DTQWs) provide a convenient platform for a realization of many topological
phases in noninteracting systems. They often offer more possibilities than systems with a static Hamiltonian.
Nevertheless, researchers are still looking for DTQW symmetries protecting topological phases and for definitions
of appropriate topological invariants. Although the majority of DTQW studies on this topic focus on the
so-called split-step quantum walk, two distinct topological phases can be observed in more basic models. Here
we infer topological properties of the basic DTQWs directly from the mapping of the Brillouin zone to the Bloch
Hamiltonian. We show that for translation-symmetric systems they can be characterized by a homotopy relative
to special points. We also propose a topological invariant corresponding to this concept. This invariant indicates
the number of edge states at the interface between two distinct phases.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

@article{Grudka2021,
title = {Quantum semipermeable barriers: Investigating Maxwell's demon toolbox},
author = {Andrzej Grudka and Paweł Kurzyński and Antoni Wójcik},
url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.104.064114},
doi = {10.1103/PhysRevE.104.064114},
year = {2021},
date = {2021-12-10},
journal = {Physical Review E},
volume = {104},
pages = {064114},
abstract = {We study quantum Maxwell's demon in a discrete space-time setup. We consider a collection of particles hopping on a one-dimensional chain and a semipermeable barrier that allows the particles to hop in only one direction. Our main result is a formulation of a local unitary dynamics describing the action of this barrier. Such dynamics utilizes an auxiliary system A and we study how properties of A influence the behavior of particles. An immediate consequence of unitarity is the fact that particles cannot be trapped on one side of the barrier forever, unless A is infinite. In addition, coherent superpositions and quantum correlations are affected once particles enter the confinement region. Finally, we show that initial superposition of A allows the barrier to act as a beam splitter.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

@article{Kurzyński2021,
title = {Weighted Bures length uncovers quantum state sensitivity},
author = {Paweł Kurzyński},
url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.104.L052202},
doi = {10.1103/PhysRevE.104.L052202},
year = {2021},
date = {2021-11-18},
journal = {Physical Review E},
volume = {104},
pages = {L052202},
abstract = {The unitarity of quantum evolutions implies that an overlap between two initial states does not change in time. This property is commonly believed to explain the apparent lack of state sensitivity in quantum theory, a feature that is prevailing in classical chaotic systems. However, classical state sensitivity is based on a distance between two trajectories in phase space which is a completely different mathematical concept than an overlap between two vectors in Hilbert space. It is possible that state sensitivity in quantum theory can be detected with the help of some special metric. Here we show that the recently introduced Weighted Bures length achieves this task. We numerically investigate a unitary cellular automaton of N interacting qubits and analyze how a single-qubit perturbation affects the evolution of WBL between the unperturbed and perturbed states. We observe a linear growth of WBL if the qubits are arranged into a cyclic graph and an exponential growth if they are arranged into a random bipartite graph.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

@article{Markiewicz2021,
title = {Borromean states in discrete-time quantum walks},
author = {Marcin Markiewicz and Marcin Karczewski and Paweł Kurzyński},
url = {https://quantum-journal.org/papers/q-2021-08-16-523/},
doi = {10.22331/q-2021-08-16-523},
year = {2021},
date = {2021-08-16},
journal = {Quantum},
volume = {5},
pages = {523},
abstract = {In the right conditions, removing one particle from a multipartite bound state can make it fall apart. This feature, known as the "Borromean property", has been recently demonstrated experimentally in Efimov states. One could expect that such peculiar behavior should be linked with the presence of strong inter-particle correlations. However, any exploration of this connection is hindered by the complexity of the physical systems exhibiting the Borromean property. To overcome this problem, we introduce a simple dynamical toy model based on a discrete-time quantum walk of many interacting particles. We show that the particles described by it need to exhibit the Greenberger-Horne-Zeillinger (GHZ) entanglement to form Borromean bound states. As this type of entanglement is very prone to particle losses, our work demonstrates an intuitive link between correlations and Borromean properties of the system. Moreover, we discuss our findings in the context of the formation of composite particles.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

@article{PhysRevA.104.012220,
title = {Nonclassical oscillations in pre- and post-selected quantum walks},
author = {Xiao-Xiao Chen and Zhe Meng and Jian Li and Jia-Zhi Yang and An-Ning Zhang and Tomasz Kopyciuk and Paweł Kurzyński},
url = {https://link.aps.org/doi/10.1103/PhysRevA.104.012220},
doi = {10.1103/PhysRevA.104.012220},
year = {2021},
date = {2021-07-28},
journal = {Phys. Rev. A},
volume = {104},
pages = {012220},
publisher = {American Physical Society},
abstract = {Quantum walks are counterparts of classical random walks. They spread faster, which can be exploited in
information processing tasks, and constitute a versatile simulation platform for many quantum systems. Yet,
some of their properties can be emulated with classical light. This raises a question: which aspects of the model
are truly nonclassical? We address it by carrying out a photonic experiment based on a pre- and post-selection paradox. The paradox implies that if somebody could choose to ask either if the particle is at position x = 0 at even time steps or at position x = d (d > 1) at odd time steps, the answer would be positive, no matter
the question asked. Therefore, the particle seems to undergo long distance oscillations despite the fact that the
model allows it to jump one position at a time. We translate this paradox into a Bell-like inequality and then into
a contextuality witness. Finally, we experimentally verify this witness up to eight standard deviations.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}